If the institution of marriage and raising a family isn’t directly implied in the phrase “life, Liberty and the Pursuit of Happiness” I don’t know what is.
It says “the right to life, Liberty and the Pursuit of Happiness”, not the guarantee thereof. Those rights mean different things to different people, so let’s not have more government guarantees of marriage of same gender, three or more, groups of pygmies, etc. Or the right not to ever be insulted by someone worshipping God in public, having a gun, etc. People have forgotten that there are no guarantees in life.
I really think the misinterpretation of that phrase has invited government into our personal lives to our detriment, and the only way to stop it is-well-to stop it-and it has to start somewhere.